DIFFERENTIAL EQUATIONS AND VECTOR CALCULUS
Budget: ₹100 – ₹400 INR
Ordinary differential equations: exact equations, equations reducible to exact equations, equations of the first order and higher degree, Clairaut's equation Differential equations of higher order: introduction to linear differential equation, Solution of
linear differential equation, linear dependence and linear independence of solution, method of solution of linear differential equation- Differential operator, solution of second order homogeneous linear differential equation with constant coefficient, solution of higher order homogeneous linear differential equations with constant coefficient.
Linear differential equation solution of non-homogeneous linear differential equations with constant coefficients using operator method, method of variation of parameters, method of undetermined coefficient, solution of Euler-Cauchy equation, simultaneous differential equations by operator method
Partial differential equation introduction to partial differential equation, method of Separation of Variables, solution of wave equation, solution of heat equation, solution of Laplace equation
Vector calculus I: limit, continuity and differentiability of vector functions, length of space curve, motion of a body or particle on a curve, gradient of a scalar field and directional derivatives, divergence and curl of vector field
Vector calculus II: line integral, Greens' theorem, surface area and Surface integral, Stokes" theorem, Gauss's divergence theorem
linear differential equation, linear dependence and linear independence of solution, method of solution of linear differential equation- Differential operator, solution of second order homogeneous linear differential equation with constant coefficient, solution of higher order homogeneous linear differential equations with constant coefficient.
Linear differential equation solution of non-homogeneous linear differential equations with constant coefficients using operator method, method of variation of parameters, method of undetermined coefficient, solution of Euler-Cauchy equation, simultaneous differential equations by operator method
Partial differential equation introduction to partial differential equation, method of Separation of Variables, solution of wave equation, solution of heat equation, solution of Laplace equation
Vector calculus I: limit, continuity and differentiability of vector functions, length of space curve, motion of a body or particle on a curve, gradient of a scalar field and directional derivatives, divergence and curl of vector field
Vector calculus II: line integral, Greens' theorem, surface area and Surface integral, Stokes" theorem, Gauss's divergence theorem